Construction of some algebras of logic by using fuzzy ideals in mv-modules

Article type: Research Article

Authors: Bakhshi, M.^a | Ahn, S. S.^{b; *} | Jun, Y. B.^c | Xin, X. L.^d | Borzooei, R. A.^e

Affiliations: [a] Department of Mathematics, University of Bojnord, Bojnord, Iran | [b] Department of Mathematics Education, Dongguk University, Seoul, Korea | [c] Department of Mathematics Education, Gyeongsang National University, Jinju, Korea | [d] Department of Mathematics, Northwest University, Xi’an, P.R. China | [e] Department of Mathematics, Shahid Beheshti University of Tehran, Tehran, Iran

Correspondence: [*] Corresponding author. S. S. Ahn, Department of Mathematics Education, Dongguk University, Seoul 04620, Korea. E-mail: [email protected].

Abstract: We study the lattice structure of fuzzy A-ideals in an mv-module M (fai (M), symbolically) and show that it is a complete Heyting lattice and so the set of its pseudocomplements forms a Boolean algebra. In the sequel, the properties of fuzzy congruences in an mv-module are investigated and using them some structural theorems are stated and proved. Finally, it is proved that fai (M) can be embedded into the lattice of fuzzy congruences.

Keywords: mv-module, fuzzy A-ideal, fuzzy congruence, distributive lattice

DOI: 10.3233/JIFS-221552

Journal: Journal of Intelligent & Fuzzy Systems, vol. 44, no. 3, pp. 4509-4519, 2023